Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C81 · Schur multiplier (H2) = C1 |
| direct product | C3⋊C8×C81 |
| unambiguous semidirect product | C3⋊(C8×C81) |
| derived | C3 ⋊ C8×C81 |
| Sylow | C3×C81 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C81 | D3 |
| commutator, hypocenter | C3 | C8×C81 |
| Frattini | C4×C27 | C3×D3 |
| Fitting | C3×C4×C81 | C2 |
| socle, prime radical | C2×C32 | C4×C27 |
| cosocle | C3×C4×C27 | C2×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C4×C81 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 92 |
| transitive degree | μt(G) = 648 |
972 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 42);